SPIN STATISTICS THEOREM AND SCATTERING IN PLANAR QUANTUM-FIELD THEORIES WITH BRAID STATISTICS

We further develop the general theory of superselection sectors and their statistics for quantum fields on three-dimensional space-time. We show that the statistics of particles that are not localizable in bounded regions of space-time (but in space-like cones) are described by braid-group, rather than permutation-group representations, unless their spins are integral or half-integral. A general connection between spin and statistics is established. Extensions of the theory to non-relativistic systems of two-dimensional condensed matter physics are sketched which makes it applicable to the fractional quantum Hall effect and certain models of high-T(c) superconductivity.